论文标题
超解决的2D应力张量场使用物理知情的U-NET保存平衡约束
Super-resolving 2D stress tensor field conserving equilibrium constraints using physics informed U-Net
论文作者
论文摘要
在有限元分析中，使用大量网格对于获得准确的结果很重要，但这是一项资源消费的任务。为了实现实时仿真和优化，希望在有限的资源中获得精细的网格分析结果。本文提出了一种超分辨率方法，该方法通过利用基于U-NET的神经网络（称为Pi-Unet）来预测低分辨率轮廓图中高分辨率的应力张量场。另外，提出的模型最大程度地减少了平衡约束的残差，从而输出了物理合理的解决方案。拟议的网络经过训练，具有简单形状的FEM结果，并通过复杂的逼真的形状进行验证，以评估概括能力。尽管Esrgan是图像超分辨率的标准模型，但在应力张量预测任务中，提出的基于U-NET的模型优于Esrgan模型。
In a finite element analysis, using a large number of grids is important to obtain accurate results, but is a resource-consuming task. Aiming to real-time simulation and optimization, it is desired to obtain fine grid analysis results within a limited resource. This paper proposes a super-resolution method that predicts a stress tensor field in a high-resolution from low-resolution contour plots by utilizing a U-Net-based neural network which is called PI-UNet. In addition, the proposed model minimizes the residual of the equilibrium constraints so that it outputs a physically reasonable solution. The proposed network is trained with FEM results of simple shapes, and is validated with a complicated realistic shape to evaluate generalization capability. Although ESRGAN is a standard model for image super-resolution, the proposed U-Net based model outperforms ESRGAN model in the stress tensor prediction task.
